Examples for the White Box Testing are:

Unit Testing,Integration Testing  and API Testing.

J2EE:Junit Open Source Tool for the Component level i.e
module level testing of the source code for the branch
coverage,decision coverage etc

Dot Net:Nunit Open Source Tool for the Unit level/component
level testing.

path tesing

Whit Box Testing:- It is done by the developers to check the
code to which they have written. 
In white box testing we do the following testing techniques

1.Statement Testing.
2. Loop Testing.
3. Path Testing.
4. Branch Testing.
5. Mutation Testing.

In Statement Testing we check all whether all the statements
are given in a correct format and in a meaningful format.
In Loop testing we check whether the assigned loop is
terminating properly in the code part. 
In Path testing each and every code has some path to flow
one path goes in one functionality and other path goes to
other functionality so here we need to check whether the
path flow is moving properly or not.
In Branch testing we check how many branches are there in
the code all the branches are moving properly
IN Mutation testing we check the standard of code like for
the working part of code remove some lines and then run the
code here we should get an error message related to the
removed lines of code - to justify whether the code is
working properly or not.


All these things need to tested by developers for there own
code before they release to QA team.